feat: correlation graph-equality congruence + induced-union bridge (union form) — #2965#2978
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…nion form)
Complete Phase A step 1 (the Fintype-instance transport):
- correlation_congr_of_eq: G₁ = G₂ ⇒ correlation G₁ p A = correlation G₂ p A,
invariant across different Fintype edgeSet instances (edgeFinset coerces to the
instance-free edgeSet). Bridges propositional graph equalities without rw's
motive obstruction.
- correlation_inducedGraph_union_inl_of_no_cross: the component-factorization
bridge stated directly on inducedGraph (Λ₁ ∪ Λ₂):
correlation (inducedGraph (Λ₁ ∪ Λ₂)) p ((A.map inl).map union)
= correlation (inducedGraph Λ₁) p A
for disjoint Λ₁,Λ₂ with no cross edge, via
inducedGraph_sum_map_eq_union_of_no_cross + correlation_congr_of_eq +
correlation_inducedGraph_sum_map_inl. This is the form usable for exhaustion
stages.
Part of #2965
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This was referenced May 26, 2026
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…2981) * feat: inducedGraph unaffected by deleting non-internal edges (Part of #2965) * feat: inducedGraph unaffected by deleting non-internal edges Add inducedGraph_deleteEdges_eq_of_not_internal: if no edge of the deleted set D has both endpoints in S, then inducedGraph (G.deleteEdges D) S = inducedGraph G S. An edge of the induced subgraph on S joins two S-vertices, so it is internal and never deleted. This is the Finset route to the bond-deletion → isolated-component bridge: deleting the cut (cross) edges between S and its complement leaves the within-S induced subgraph (hence its correlations) intact, and the bond-deleted graph then has no cross edges, so correlation_inducedGraph_union_inl_of_no_cross (#2978) applies directly to it — reusing the working inducedGraph/Finset machinery instead of the instance-pathological Equiv.sumCompl predicate route (#2980). Part of #2965 Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.7 <noreply@anthropic.com>
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* feat: straddle-set no-cross + not-internal facts (Part of #2965) * feat: straddle-set no-cross + not-internal facts Add two graph-level facts about the straddle (cut) edge set of induce_sum_map_sumCompl_eq_deleteEdges: - straddle_not_mem_of_same_side: p a ↔ p b ⇒ s(a,b) ∉ straddle (the deleted set contains no same-side edge), feeding inducedGraph_deleteEdges_eq_of_not_internal. - deleteEdges_straddle_no_cross: p a, ¬p b ⇒ ¬(G.deleteEdges {straddle}).Adj a b (the bond-deleted graph disconnects the two sides), the no-cross hypothesis for correlation_inducedGraph_union_inl_of_no_cross applied to G.deleteEdges {straddle}. Pure adjacency facts (no Fintype), bridging #2979/#2981/#2978 toward the bond-deletion → isolated-component capstone via the working inducedGraph route. Part of #2965 Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.7 <noreply@anthropic.com>
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…apstone, Finset route) — #2965 (#2983) * feat: bond-deleted correlation = isolated induced subgraph (Finset route) (Part of #2965) * feat: bond-deleted correlation = isolated induced subgraph (Phase A capstone, Finset route) Add correlation_inducedGraph_deleteEdges_union_inl: for S ⊆ W, deleting the cut edges between S and Sᶜ gives correlation (inducedGraph (G.deleteEdges {straddle S}) (S ∪ Sᶜ)) p ((A.map inl).map union) = correlation (inducedGraph G S) p A — the bond-deleted model's correlation of an S-supported observable equals the correlation in the isolated induced subgraph on S of the original model. Assembled from correlation_inducedGraph_union_inl_of_no_cross (#2978) ∘ correlation_congr_of_eq (inducedGraph_deleteEdges_eq_of_not_internal, #2981), with no-cross/not-internal hypotheses discharged by deleteEdges_straddle_no_cross / straddle_not_mem_of_same_side (#2982). Reuses the working inducedGraph/Finset machinery, sidestepping the Equiv.sumCompl instance pathology (#2980) entirely. This is the Issue #2965 Phase A component-factorization capstone: combined with the ball-boundary bond-deletion increment correlation_sub_deleteEdges_le_derivBound (#2974), it yields the per-stage exhaustion increment bound. Part of #2965 Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.7 <noreply@anthropic.com>
This was referenced May 26, 2026
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Part of #2965
Completes Phase A step 1 (Fintype-instance transport), in
InducedUnion.lean:correlation_congr_of_eq:G₁ = G₂ ⇒ correlation G₁ p A = correlation G₂ p A, invariant across differentFintype edgeSetinstances (edgeFinsetcoerces to the instance-freeedgeSet). Bridges propositional graph equalities withoutrw's motive obstruction.correlation_inducedGraph_union_inl_of_no_cross: the component-factorization bridge stated directly oninducedGraph (Λ₁ ∪ Λ₂):correlation (inducedGraph (Λ₁ ∪ Λ₂)) p ((A.map inl).map union) = correlation (inducedGraph Λ₁) p Afor disjointΛ₁,Λ₂with no cross edge — viainducedGraph_sum_map_eq_union_of_no_cross(feat: induced-union splits as disjoint sum under no cross edges — #2965 #2977) +correlation_congr_of_eq+correlation_inducedGraph_sum_map_inl. The form usable for exhaustion stages.lake build IsingModel.AmbientLatticeSum.InducedUniongreen, sorry 0, file linter-clean, tex compiles.🤖 Generated with Claude Code